1. LESSON 81 – WORKING WITH SYSTEMS OF EQUATIONS
HL2 Math - Santowski

2. EXAMPLE #1
Given the system
Show that the solution to this system is

3. EXAMPLE #1 (CONTINUED)
Hence, or otherwise, solve the complex system

4. EXAMPLE #1 (CONTINUED)
Hence, or otherwise, solve the complex system

5. EXAMPLE #2 Solve, and then interpret, the system defined by
Use the method of:
(a) Substitution
(b) elimination

6. EXAMPLE #2 Solve the system defined by Use the method of:
(a) Substitution
(b) elimination

7. EXAMPLE #2 – GEOMETRIC INTERPRETATION
From h3d/

8. SOLUTIONS TO THREE SIMULTANEOUS EQUATIONS
When solving systems where we have three variables (as in the geometric idea of having three planes in space), we have three possible scenarios:
(a) one unique ordered triplet (a “point” that satisfies all three equations – a unique “intersection” point)
(b) NO ordered triplet of real numbers that satisfies all three equations (no unique “intersection” point)
(c) Infinitely many ordered triplets that satisfy all three equations

9. EXAMPLE #3
Use the Gaussian method of solving the simultaneous equations:

10. EXAMPLE #3
Use the Gaussian method of solving the simultaneous equations:

11. EXAMPLE #3 – SOLUTION FROM TI-84
Use the Gaussian method of solving the simultaneous equations:

12. EXAMPLE #4
Discuss all the possible types of solutions of this system of equations with respect to the real parameter K.

13. EXAMPLE #4
Discuss all the possible types of solutions of this system of equations with respect to the real parameter K.

14. GEOMETRIC INTERPRETATIONS

15. GEOMETRIC INTERPRETATIONS

16. INTERSECTION OF THREE PLANES – CASE 1

17. INTERSECTION OF THREE PLANES – CASE 1

18. INTERSECTION OF THREE PLANES – CASE 2

19. INTERSECTION OF THREE PLANES – CASE 2

20. INTERSECTION OF THREE PLANES – CASE 3

21. INTERSECTION OF THREE PLANES – CASE 3

22. INTERSECTION OF PLANES - PRACTICE